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"""

Diffuse IAM Calculation

=======================

Integrating an IAM model across angles to determine the overall reflection

loss for diffuse irradiance.

"""

# %%

# The fraction of light reflected from the front of a module depends on the

# angle of incidence (AOI) of the light compared to the panel surface. The

# greater the AOI, the larger the reflected fraction is. The incident angle

# modifier (IAM) is defined as the ratio of light transmitted at the given

# AOI to transmitted light at normal incidence.

# Several models exist to calculate the IAM for a given incidence

# angle (e.g. :py:func:`pvlib.iam.ashrae`, :py:func:`pvlib.iam.martin_ruiz`,

# :py:func:`pvlib.iam.sapm`, :py:func:`pvlib.iam.physical`).

# However, evaluating the IAM for diffuse light is

# not as straightforward because it comes from all directions and therefore

# has a range of angles of incidence. Here we show how to integrate the effect

# of AOI reflection across this AOI range using the process described in [1]_.

# In particular, we will recreate Figures 3, 4, and 5 in that paper.

#

# References

# ----------

# .. [1] B. Marion "Numerical method for angle-of-incidence correction

# factors for diffuse radiation incident photovoltaic modules",

# Solar Energy, Volume 147, Pages 344-348. 2017.

# DOI: 10.1016/j.solener.2017.03.027

#

# .. [2] Duffie, John A. & Beckman, William A. (2013). Solar Engineering

# of Thermal Processes. DOI: 10.1002/9781118671603

from pvlib.iam import marion_diffuse, physical

import numpy as np

import matplotlib.pyplot as plt

# %%

# IAM Model

# ---------

#

# The IAM model used to generate the figures in [1]_ uses Snell's, Fresnel's,

# and Beer's laws to determine the fraction of light transmitted through the

# air-glass interface as a function of AOI.

# The function :py:func:`pvlib.iam.physical` implements this model, except it

# also includes an exponential term to model attenuation in the glazing layer.

# To be faithful to Marion's implementation, we will disable this extinction

# term by setting the attenuation coefficient ``K`` parameter to zero.

# For more details on this IAM model, see [2]_.

#

# Marion generated diffuse irradiance modifiers for two cases: a standard

# uncoated glass with index of refraction n=1.526 and a glass with

# anti-reflective (AR) coating with n=1.3.

# Comparing the IAM model across AOI recreates Figure 3 in [1]_:

aoi = np.arange(0, 91)

iam_no_coating = physical(aoi, n=1.526, K=0)

iam_ar_coating = physical(aoi, n=1.3, K=0)

plt.plot(aoi, iam_ar_coating, c='b', label='$F_b$, AR coated, n=1.3')

plt.plot(aoi, iam_no_coating, c='r', label='$F_b$, uncoated, n=1.526')

plt.xlabel(r'Angle-of-Incidence, AOI $(\degree)$')

plt.ylabel('Diffuse Incidence Angle Modifier')

plt.legend()

plt.ylim([0, 1.2])

plt.grid()

# %%

# Diffuse sky, ground, and horizon IAM

# ------------------------------------

#

# Now that we have an AOI model, we use :py:func:`pvlib.iam.marion_diffuse`

# to integrate it across solid angle and determine diffuse irradiance IAM.

# Marion defines three types of diffuse irradiance:

# sky, horizon, and ground-reflected. The diffuse IAM value is evaluated

# independently for each type.

tilts = np.arange(0, 91, 2.5)

# marion_diffuse calculates all three IAM values (sky, horizon, ground)

iam_no_coating = marion_diffuse('physical', tilts, n=1.526, K=0)

iam_ar_coating = marion_diffuse('physical', tilts, n=1.3, K=0)

# %%

# First we recreate Figure 4 in [1]_, showing the dependence of the sky diffuse

# incidence angle modifier on module tilt.

plt.plot(tilts, iam_ar_coating['sky'], c='b', marker='^',

label='$F_{sky}$, AR coated, n=1.3')

plt.plot(tilts, iam_no_coating['sky'], c='r', marker='x',

label='$F_{sky}$, uncoated, n=1.526')

plt.ylim([0.9, 1.0])

plt.xlabel(r'PV Module Tilt, $\beta (\degree)$')

plt.ylabel('Diffuse Incidence Angle Modifier')

plt.grid()

plt.legend()

plt.show()

# %%

# Now we recreate Figure 5 in [1]_, showing the dependence of the diffuse iam

# values for horizon and ground diffuse irradiance on module tilt. Note that

# :py:func:`pvlib.iam.marion_diffuse` defaults to using 1800 points for the

# horizon case (instead of 180 like the others) to match [1]_.

plt.plot(tilts, iam_ar_coating['horizon'], c='b', marker='^',

label='$F_{hor}$, AR coated, n=1.3')

plt.plot(tilts, iam_no_coating['horizon'], c='r', marker='x',

label='$F_{hor}$, uncoated, n=1.526')

plt.plot(tilts, iam_ar_coating['ground'], c='b', marker='s',

label='$F_{grd}$, AR coated, n=1.3')

plt.plot(tilts, iam_no_coating['ground'], c='r', marker='+',

label='$F_{grd}$, uncoated, n=1.526')

plt.xlabel(r'PV Module Tilt, $\beta (\degree)$')

plt.ylabel('Diffuse Incidence Angle Modifier')

plt.grid()

plt.legend()

plt.show()